Normally Luto tells you in the cutscene which activates the quest the place you have to go. If that doesn't work, try 'talk about quests' with your NPC at the rendezvous point or ask Luto 'Something new?'. If that both doesn't work you could try to talk to the Past Event Watcher Bard in Upper Jeuno (Tinjue near the gate to Battalia Downs) to rewatch the cutscene of this quest.
And if even that doesn't work ... well, I fear than you have to look at all three places and to check all three ??? to see which spawns the Metallic Slime for you.
When you go to the ??? you don't have to have your NPC called, he will appear automatically after the cutscene from the ???. Like every other NM-fight in this quest: Don't let your NPC die or you will have to do the fight a second time in the next Vana'diel-day.
You can increase your friendship everytime you call your NPC via the Signal/Tactics Pearl and with the option 'lets chat' at the Rendezvous Point, although the later one works just once each RL-day.